Energy Transfer in Multi Field Inflation and Cosmological Perturbations

TL;DR

The paper develops a two-field model to capture energy transfer from the inflaton to a boundary fluid during cascade inflation, implementing a step-like change in the inflaton potential and a coupled exponential potential for the boundary field. It demonstrates that the energy transfer induces a sharp turn in field space, generating strong coupling between adiabatic and isocurvature perturbations, which modulates the curvature power spectrum with damped oscillations and seeds curvature for pre-collision modes while the isocurvature component decays over time. The analysis explores how the modulation, its decay, and the tensor signature depend on the transferred energy, the step width, and the boundary fluid equation of state, including radiation, matter, and cosmic strings cases, highlighting observable imprints in the primordial spectrum. Overall, the work highlights how backreaction from brane-boundary energy transfer can leave distinctive, scale-dependent signatures in both scalar and tensor perturbations within a controlled two-field framework.

Abstract

In cascade inflation and some other string inflation models, collisions of mobile branes with other branes or orbifold planes occur and lead to interesting cosmological signatures. The fundamental M/string-theory description of these collisions is still lacking but it is clear that the inflaton looses part of its energy to some form of brane matter, e.g. a component of tensionless strings. In the absence of a fundamental description, we assume a general barotropic fluid on the brane, which absorbs part of the inflaton's energy. The fluid is modeled by a scalar with a suitable exponential potential to arrive at a full-fledged field theory model. We study numerically the impact of the energy transfer from the inflaton to the scalar on curvature and isocurvature perturbations and demonstrate explicitly that the curvature power spectrum gets modulated by oscillations which damp away toward smaller scales. Even though, the contribution of isocurvature perturbations decays toward the end of inflation, they induce curvature perturbations on scales that exit the horizon before the collision. We consider cases where the scalar behaves like radiation, matter or a web of cosmic strings and discuss the differences in the resulting power spectra.

Figures (7)

• Figure 1: The graphs show the evolution of the Hubble parameter and the first slow-roll parameter as a function of the number of e-foldings. Around $N_e\simeq 10$ the inflaton's potential energy $(U_i-U_f)$ is transferred to the $\chi$ field.
• Figure 2: The left graph shows the evolution of the fields $\varphi$ and $\chi$. They move upwards from left to right along the black trajectory, whose very first part coincides with the $\varphi$ axis. The right graph displays $d\theta/dN_e$ as a function of the number of e-foldings $N_e$. A sharp turn in field space at the collision is clearly visible.
• Figure 3: The left and right graphs show the evolution of $|Q_{\sigma}^{\rm prim}|$, $|Q_{\sigma}^{\rm ind}|$ and $|\delta s^{\rm prim}|$
• Figure 4: The left graph shows the adiabatic spectrum vs. $\log(k/a_0H_0)$ for the modes that exit the horizon around the decay time. It is assumed that the energy of the decay products redshifts as radiation, $U_f/U_i=0.932$ and $\Delta \phi=10^{-3} M_{\rm P}$. The right graph shows the adiabatic power spectrum for the single field case with an inflaton potential having a step of equal height. The oscillations in the single field case last much longer than in the two field case with ET.
• Figure 5: The left graph shows the curvature spectra vs. $\log(k/a_0H_0)$ for $\Delta U/U_i=0.068$ and $\Delta U/U_i=0.03$. The right graph shows the adiabatic power spectra vs. $\log(k/a_0H_0)$ for $\Delta\varphi=10^{-2} M_{\rm P}$ (black solid line) and $\Delta\varphi=10^{-3} M_{\rm P}$ (dashed grey line)